Triangulation Method for Approximate Solving of Variational Problems in Nonlinear Elasticity
A variational problem for the minimum of the stored energy functional is considered in the framework of the nonlinear theory of elasticity, taking into account admissible deformations. An algorithm for solving this problem is proposed, based on the use of a polygonal partition of the computational d...
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| Format: | Article |
| Language: | English |
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Irkutsk State University
2023-09-01
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| Series: | Известия Иркутского государственного университета: Серия "Математика" |
| Subjects: | |
| Online Access: | http://mathizv.isu.ru/en/article/file?id=1459 |
| _version_ | 1797685161838510080 |
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| author | V. A. Klyachin V. V. Kuzmin E. V. Khizhnyakova |
| author_facet | V. A. Klyachin V. V. Kuzmin E. V. Khizhnyakova |
| author_sort | V. A. Klyachin |
| collection | DOAJ |
| description | A variational problem for the minimum of the stored energy functional is considered in the framework of the nonlinear theory of elasticity, taking into account admissible deformations. An algorithm for solving this problem is proposed, based on the use of a polygonal partition of the computational domain by the Delaunay triangulation method. Conditions for the convergence of the method to a local minimum in the class of piecewise affine mappings are found. |
| first_indexed | 2024-03-12T00:41:05Z |
| format | Article |
| id | doaj.art-4707718faf434bf4bdd87c50ba97ac46 |
| institution | Directory Open Access Journal |
| issn | 1997-7670 2541-8785 |
| language | English |
| last_indexed | 2024-03-12T00:41:05Z |
| publishDate | 2023-09-01 |
| publisher | Irkutsk State University |
| record_format | Article |
| series | Известия Иркутского государственного университета: Серия "Математика" |
| spelling | doaj.art-4707718faf434bf4bdd87c50ba97ac462023-09-15T07:32:19ZengIrkutsk State UniversityИзвестия Иркутского государственного университета: Серия "Математика"1997-76702541-87852023-09-014515472https://doi.org/10.26516/1997-7670.2023.45.54Triangulation Method for Approximate Solving of Variational Problems in Nonlinear ElasticityV. A. KlyachinV. V. KuzminE. V. KhizhnyakovaA variational problem for the minimum of the stored energy functional is considered in the framework of the nonlinear theory of elasticity, taking into account admissible deformations. An algorithm for solving this problem is proposed, based on the use of a polygonal partition of the computational domain by the Delaunay triangulation method. Conditions for the convergence of the method to a local minimum in the class of piecewise affine mappings are found.http://mathizv.isu.ru/en/article/file?id=1459stored energy functionalvariational problemgradient descent methoddelaunay triangulationfinite element method |
| spellingShingle | V. A. Klyachin V. V. Kuzmin E. V. Khizhnyakova Triangulation Method for Approximate Solving of Variational Problems in Nonlinear Elasticity Известия Иркутского государственного университета: Серия "Математика" stored energy functional variational problem gradient descent method delaunay triangulation finite element method |
| title | Triangulation Method for Approximate Solving of Variational Problems in Nonlinear Elasticity |
| title_full | Triangulation Method for Approximate Solving of Variational Problems in Nonlinear Elasticity |
| title_fullStr | Triangulation Method for Approximate Solving of Variational Problems in Nonlinear Elasticity |
| title_full_unstemmed | Triangulation Method for Approximate Solving of Variational Problems in Nonlinear Elasticity |
| title_short | Triangulation Method for Approximate Solving of Variational Problems in Nonlinear Elasticity |
| title_sort | triangulation method for approximate solving of variational problems in nonlinear elasticity |
| topic | stored energy functional variational problem gradient descent method delaunay triangulation finite element method |
| url | http://mathizv.isu.ru/en/article/file?id=1459 |
| work_keys_str_mv | AT vaklyachin triangulationmethodforapproximatesolvingofvariationalproblemsinnonlinearelasticity AT vvkuzmin triangulationmethodforapproximatesolvingofvariationalproblemsinnonlinearelasticity AT evkhizhnyakova triangulationmethodforapproximatesolvingofvariationalproblemsinnonlinearelasticity |